Re: If A is invertible then A+B and I+BA^-1 are both invertible or both non-invertibl

Originally Posted by Jester

Consider

and .

Perhaps you did not understand the question. The A and B you give are invertible matrices. A+ B is not and I+ BA^-1 is not either, just as the "theorem" says. This is an example for which the statement is true but an example doesn't prove anything.